Regarding the need for a systematic taxonomy of triangles

This document (ver. 2) is the inaugural preprint of the "Not Just Triangles" (NJT) Research Project. It identifies a fundamental gap in classical geometry: the absence of a universal, hierarchical classification system for triangles that encompasses their full metric, topological, and relational properties. Abstract:The triangle, a fundamental geometric entity, remains without a universal, hierarchical classification system that encompasses the full spectrum of its metric, topological, and relational properties. This preprint identifies this critical gap and introduces the NJT Project — a structured research endeavor aimed at developing a comprehensive taxonomy. Moving beyond traditional classifications based solely on sides or angles, the project proposes a multi-level, feature-based framework capable of describing triangles in both static and dynamic environments. This work outlines the project's philosophy, its potential applications in computer vision, computational geometry, and pattern recognition. The NJT Project aims to create:1. A multi-criteria hierarchical taxonomy for triangles, integrating basic (angles/sides), metric, topological, and combinatorial criteria.2. A formal notation system for the unambiguous, machine-readable description of any triangle type.3. An open knowledge base and interactive visualizer to serve as a practical tool for research and education. Content of This Upload:This pdf file contains the complete first preprint, which includes:- A detailed justification of the research gap in existing triangle classifications.- The formal statement of the project's goals and methodological outline.- Discussion of the didactic significance of creating a systematic taxonomy.- The full text with sections: Introduction, The Research Gap, Aims of the Project, Methodological Outline, Didactic Significance, and Conclusion. Significance and Potential Impact:This work lays the philosophical and conceptual foundation for a paradigm shift in how we categorize and understand triangles. The proposed taxonomy is designed to become a foundational tool for fields that utilize triangular structures as building blocks, including:- Computational Geometry & Computer Graphics- Computer Vision & Pattern Recognition- Topological Data Analysis & Network Theory- Mathematical Education and Interdisciplinary Research Note: This is Preprint #1. It announces the project. Subsequent preprints will detail specific taxonomic modules (e.g., the Path-Dependent Taxonomy - PDT) and their implementations. Bilingual Publication Structure: This work is presented in a bilingual format (English/Russian), offering complete parallel texts of the abstract, introduction, core methodology, results, and conclusions. This approach ensures broad accessibility and facilitates dissemination within the international community as well as among Russian-speaking researchers.